Finite Group Databasebeta

← #23764560

Subgroups — #23764560

Order 10112.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099191C211yesmaximal, characteristic
2#19098573C211yesmaximal, characteristic
3#19098571C211yesmaximal, characteristic
4#19098469C211yesmaximal, characteristic
5#19098331C211yesmaximal, characteristic
6#19098323C211yesmaximal, characteristic
7#339×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10#14579161—21no—
11#14579160—21no—
12#14579153—21no—
13#14579152—21no—
14#14579138—22no—
15#14579120C2211yescharacteristic
16C2×C4⋊Dic79C2211yescharacteristic
17#14579086—21no—
18#14579086—21no—
19#14579084—21no—
20#14579084—21no—
21C79⋊#95—22no—
22C2×M16×C79C2211yescharacteristic
23#117×C79C2211yescharacteristic
24C2×C42×C79C2211yescharacteristic
25C2×Dic158—22no—
26C2×Dic158—21no—
27C2×Dic158—21no—
28C2×Dic158—21no—
29C2×Dic158—21no—
30C2×Dic158—21no—
31C2×Dic158Q812yescomplemented
32C22×Dic79—21no—
33C22×Dic79D412yes—
34#11929608—21no—
35#11929608—21no—
36C2×C79⋊C8—21no—
37C4⋊Dic79—22no—
38C4⋊Dic79—21no—
39C4⋊Dic79—21no—
40C4⋊Dic79D411yescharacteristic
41C4⋊Dic79D411yescharacteristic
42Dic79⋊C4—22no—
43Dic79⋊C4—22no—
44C22⋊Dic79—21no—
45C4×Dic79—21no—
46C22×C4×C79—21no—
47C22×C4×C79C2311yescharacteristic
48M16×C79—21no—
49M16×C79—21no—
50C2×C8×C79—21no—
51C4⋊C4×C79D411yescharacteristic
52C4⋊C4×C79D411yescharacteristic
53C22⋊C4×C79—21no—
54C42×C79—21no—
55C42×C79—21no—
56C42×C79—21no—
57C23×C79C2×D411yescharacteristic
58C2×C4×C79—22no—
59C2×C4×C79—21no—
60C2×C4×C79—21no—
61C2×C4×C79—41no—
62C2×C4×C79—41no—
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2×Q811yescharacteristic
66C2×C4×C79#4111yescharacteristic
67C2×C4×C79#4111yescharacteristic
68C2×C4×C79#4111yescharacteristic
69C2×Dic79—21no—
70C2×Dic79—21no—
71C2×Dic79—22no—
72C2×Dic79—22no—
73C2×Dic79—41no—
74C2×Dic79—41no—
75C2×Dic79—42no—
76Dic158—22no—
77Dic158—22no—
78Dic158—41no—
79Dic158—41no—
80Dic158—82no—
81C8×C79—41no—
82C79⋊C8—41no—
83C22×C79—21no—
84C22×C79—21no—
85C22×C79#12011yescharacteristic
86C22×C79C22⋊Q811yescharacteristic
87C22×C79#12411yescharacteristic
88C4×C79—42no—
89C4×C79—41no—
90C4×C79—41no—
91C4×C79C22⋊Q811yescharacteristic
92C4×C79C22⋊Q811yescharacteristic
93C4×C79#12411yescharacteristic
94C4×C79#12411yescharacteristic
95Dic79—42no—
96Dic79—41no—
97Dic79—42no—
98Dic79—41no—
99C2×C79—21no—
100C2×C79—21no—
101C2×C79#39311yescharacteristic
102C2×C79#45511yescharacteristic
103C2×C79#45611yescharacteristic
104#2028—791nomaximal, Sylow
105C79#202811yescharacteristic, complemented, Sylow
106#544—791no—
107#419—791no—
108#419—791no—
109#391—791no—
110#343—791no—
111#339—791no—
112#339D7911yescharacteristic
113C22×Q8—791no—
114C2×M16—791no—
115C2×M16C2×D7911yescharacteristic
116C4⋊Q8—1581no—
117C4⋊Q8—1581no—
118#125—1581no—
119#125—1581no—
120C22⋊Q8—1582no—
121#117—791no—
122#117C2×D7911yescharacteristic
123C2×C4⋊C4—791no—
124C2×C42C2×D7911yescharacteristic
125#103—1581no—
126#103—1581no—
127#103—1581no—
128#103—1581no—
129#95—1582no—
130C2×Q8—792no—
131C2×Q8—1582no—
132C2×Q8—1581no—
133C2×Q8—1581no—
134C2×Q8—1581no—
135C2×Q8—1581no—
136C2×Q8—1581no—
137C22×C4—21no—
138C22×C4—792no—
139C22×C4—1581no—
140C22×C4C22×D7911yescharacteristic
141M16—21no—
142M16—21no—
143M16—1581no—
144M16—1581no—
145C2×C8—21no—
146C2×C8—1581no—
147C4⋊C4—791no—
148C4⋊C4—791no—
149C4⋊C4—1582no—
150C4⋊C4—1582no—
151C4⋊C4—1582no—
152C4⋊C4—1581no—
153C4⋊C4—1581no—
154C4⋊C4D31611yescharacteristic
155C4⋊C4D31611yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—1581no—
158C42—21no—
159C42—21no—
160C42—21no—
161C42—1581no—
162C23D4×D7911yescharacteristic
163Q8—3161no—
164Q8—3161no—
165Q8—6322no—
166Q8—1582no—
167Q8—1582no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3161no—
174C2×C4—3161no—
175C2×C4—3162no—
176C2×C4—1581no—
177C2×C4—1581no—
178C2×C4—1582no—
179C2×C4—1582no—
180C2×C4D4×D7911yescharacteristic
181C2×C4C2×D31611yescharacteristic
182C2×C4Q8×D7911yescharacteristic
183C2×C4#1192962311yescharacteristic
184C2×C4#1192962411yescharacteristic
185C2×C4#1192962411yescharacteristic
186C8—41no—
187C8—3161no—
188C22—21no—
189C22—21no—
190C22#1457913111yescharacteristic
191C22#1457913911yescharacteristic
192C22#1457914711yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—3162no—
197C4—3162no—
198C4—3161no—
199C4—3161no—
200C4#1457913911yescharacteristic
201C4#1457914111yescharacteristic
202C4#1457914711yescharacteristic
203C4#1457914911yescharacteristic
204C2—21no—
205C2—21no—
206C2#1909847611yescharacteristic
207C2#1909874211yescharacteristic
208C2#1909874711yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#339×C79C2
socleC22×C79#120
prime radicalC23×C79C2×D4
hypercenter#339D79
hypocenterC79#2028
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
31. C2×Dic158Q8semidirect
105. C79#2028semidirect